Bounds on the weight hierarchies of linear codes of dimension 4

The weight hierarchy of a linear [n,k;q] code C over GF(q) is the sequence (d/sub 1/,d/sub 2/,...,d/sub k/) where d/sub r/ is the smallest support of an r-dimensional subcode of C. The codes of dimension 4 are collected in classes. For each class bounds and extremal codes are discussed.